T2.T? 5.
UJU.4J
A number consists of two digits. The digit at the ten's place is
two times the digit at the unit's place. The number formed by
reversing the digit is 27 less than the original number. Find
the original number?
[CMAT 2011]​

9514 1404 393

  63

Step-by-step explanation:

Reversing the digits changes the value by a factor of 9 times the difference in the digit values. Here, this means the digits differ by 27/9 = 3. If one digit is double the other, the higher digit is 2×3 = 6.

The number is 63.

If you like, you can work through the algebra of it. Let the original number have tens digit x and ones digit y.

  original number value = 10x +y

  reversed number value = 10y +x

  difference of values = 27 = (10x +y) -(10y +x) = 9(x -y)

The tens digit is twice the ones digit, so we have ...

  x = 2y

Substituting in the difference equation, we have ...

  27 = 9(x -y)

  3 = (2y -y) = y . . . . . divide by 9, substitute for x

  x = 2(3) = 6

The number is 10x+y = 63.